Let f:N + N be defined by the recursive definition: Base case: f(0) = 7 Recursive...
(1 point) (3 Marks] Note that 0 € N. Give a recursive function f:N → N that represents the sequence ao, 21, 22, az... if an 10n + 1. (1 point) [3 Marks] Find mod(31004 + 1004!, 11). A. I am finished this question
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f:N + N that represents the sequence ao, 21, 22, az... if an = 10n + 1.
Note that 0 EN Give a recursive function f:N → N that represents the sequence ao, 21, 22, 23... if an 10n +1.
Suppose f:N → N satisfies the recurrence f(n+1) = f(n) 7. Note that this is not enough information to define the function, since we don't have an initial condition. For each of the initial conditions below, find the value of f(7). a. f(0) = 1. $(7) = b. f(0) = 5. f(7) = c. f(0) = 19. f(7) = d. f(0) = 249. f(7) =
6. Find a recursive definition for the following sequences defined by the closed formulas: (a) an = -3 - 5 (b) an = (-5)-31 (C) an = n! 21
Please do exercise 129: Exercise 128: Define r:N + N by r(n) = next(next(n)). Let f:N → N be the unique function that satisfies f(0) = 2 and f(next(n)) =r(f(n)) for all n E N. 102 1. Prove that f(3) = 8. 2. Prove that 2 <f(n) for all n E N. Exercise 129: Define r and f as in Exercise 128. Assume that x + y. Define r' = {(x,y),(y,x)}. Let g:N + {x,y} be the unique function that...
The recursive definition of a Fibonacci Number is F(n) = F(n - 1) + F(n - 2), where F(0) = 1 and F(1) = 1. What is the value of Fib(3)?
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t2 0. Then the integral D{f(t)} = ( strit) at is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. f(t) = {-1, Ost<1 f(t) = { 1, 2 1 L{FC)} = (s > 0)
4. Define a function f:N → Z by tof n/2 if n is even 1-(n + 1)/2 if n is odd. f(n) = Show that f is a bijection. 11 ] 7. Let X = R XR and let R be a relation on X defined as follows ((x,y),(w,z)) ER 4 IC ER\ {0} (w = cx and z = cy.) Is R reflexive? Symmetric? Transitive? An equivalence relation? Explain each of your answers. Describe the equivalence classes [(0,0)]R and...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...